The campaign will net you a certain amount of loot your first time through. The gold chests in each planet will give you an item when you open it the first (only) time. Bounties that reset daily might reward you with gear. Completing strikes will reward you with gear. Killing enemies has a chance to reward you with gear. PvP has a chance to reward you with gear. I've never done a Nightfall, but I'm banking on them giving you gear, not only as a reward, but the enemies within are extremely likely to drop loot. Nightfalls are the strikes you encounter on your way to 20 but revamped to be 20+. For example: The first Nightfall is a level 20 or 21 (i forget) encounter "The Devil's Lair". Well the very first strike you go to is "The Devil's Lair" @ level 6 and level 8 (for hard mode) if you toggle the higher level function. I think all missions have this toggle function in case you level up via PvP or free roaming and you want your next story mission to be on par with your abilities / level. I don't remember the following names, but the next Nightfall is like level 22 which is just the 2nd strike which you get to around level 10 or so. Next Nightfall = 23+ which is the third strike, etc.

1. Kill shit.
2. Keep an eye out for green orbs, blue glitter, and generally anything that pops out of an enemy when they die.
3. Chest. There are chest hiding around the game that provide you with all kinds of goodies.
4. Completing levels, strikes, public events, etc.
5. Completing task such as bounties. Bounties are what you would call challenges... sort of. You go talk to this guy at the Tower and he has multiple bounties you can choose to complete. Some are for Crucible only. These can have you doing anything from getting X amount of melee kills without dying to killing X amount of this type of enemy. You can carry up to 5 bounties. They change daily. You have to return to the bounty guy once you have completed the bounty to collect your reward.
And of that was all in the beta. Also, you can work for certain factions that also give you gear (loot). There's no telling what else they have in store for us on release.